Echoing Bill Rouse's comments...
In an Amel with standard wiring, the connection of shore power would have nothing what ever to do with the engine starting--or not. Also, in a boat with Amel standard wiring, the state of the 24 Volt system is not at all connected with the ability of the engine to start, or to run.
Based on your description of the symptoms you observe, it would seem your wring has been changed in significant ways. Without knowing HOW your system has been changed, it is virtually impossible to offer specific advice.
I think you are probably right to be concerned that things are not as they should be, but without knowing how your batteries and engine are wired I am not sure how we can help remotely.
Are you located in a place you can get in contact with a marine electrician who is familiar with Amel systems?